jimandme -
Figure on getting 1.5 - 2.0 hours of cooking time per green cylinder (assuming it's the 14-16 ounce variety frequently used with Coleman's). If it was my group of 4, I'm figuring on 30 minutes of use per breakfast and 60 minutes per supper. Over nine days, that's 8 breakfasts X 30 minutes = 240 minutes AND that's 8 suppers X 60 minutes = 480 minutes. Grand total = 720 minutes or 12 hours of use. So, that's 6 cylinders.
Of course, you may be cooking over a campfire for some meals. For other meals you may only need to heat up a little water to pour into oatmeal or a bag of dehydrated food. To the extent you do those things, your need for cylinders goes DOWN. Frankly, I'd feel pretty safe with 5 cylinders (generally speaking) and possibly even 4.
On the other hand, your need for cylinders goes UP if you get one or two that develop "leaks". I had two go bad on me on a single trip one year and found myself cooking over a campfire to compensate. Fortunately, there was no fire ban going on.
Bottom line: it's something of a crap shoot. You make your best guess re: actual cooking minutes, apply the burn time per cylinder, then hope you get lucky.
As for me, I've started using Kelly Kettles as my "back-up system." For fixing coffee and simply heating water for eat-in-the-bag meals, you can't beat them. You can cook on them, too, but not nearly as well as with gas.
Jimbo